How to join more bones in a armature together
The connected bones are a Parent/child relationship: a Parent can have lots of childrens but a child can have only one parent: from the tip of a bone you can extrude (or connect) more than one bone, but you can't connect two or more bones to the base of another bone (it would have more than one parent).

Usually a complex facial rig is made of shapekeys; each shape key can be controlled by one or more bones using drivers: so you will have a rig made of deforming bones (the classic way) and non deforming bones (to drive shape keys).

Don't be afraid of drivers: they look more complicated than they are, and they're very very useful.